Document Zbl 1482.74083

<!doctype html> <html lang="en"> <head> <meta charset="utf-8"> <title>Document Zbl 1482.74083 - zbMATH Open</title> <meta name="viewport" content="width=device-width, minimum-scale=0.1, maximum-scale=5.0"> <meta name="robots" content="noarchive, noindex"> <meta name="referrer" content="origin-when-cross-origin"> <link href="https://static.zbmath.org/contrib/bootstrap/v3.3.7/css/bootstrap.min.css" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/contrib/bootstrap/v3.3.7/css/bootstrap-theme.min.css" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.css" rel="stylesheet" media="screen,print"> <link rel="stylesheet" href="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/css/bootstrap-select.min.css"> <link href="/static/css/smoothness/jquery-ui-1.10.1.custom.min.css" rel="stylesheet" media="screen"> <link href="/static/styles.css?v=20241024" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/zbMathJax/v0.1.38/zbmathjax.css" rel="stylesheet" media="screen,print"> <link rel="shortcut icon" href="/static/zbmath.ico"> <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "Organization", "url": "https://zbmath.org/", "logo": "https://zbmath.org/static/zbMATH.png" } </script> </head> <body> <div id="line"></div> <span id="clear" style="cursor: pointer;">×</span> <div id="page"> <div id="head"> <nav id="menu" class="navbar navbar-default"> <div class="container-fluid"> <div class="navbar-header"> <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#zbnav" aria-expanded="false"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar"></span> <span class="icon-bar"></span> <span class="icon-bar"></span> </button> <a class="navbar-brand" href="#"> <img class="logo" src="/static/zbmath.gif" alt="zbMATH Open logo"> </a> </div> <div id="zbnav" class="collapse navbar-collapse"> <ul class="nav navbar-nav pages"> <li class="about"> <a href="/about/">About</a> </li> <li class="frequently-asked-questions"> <a href="/frequently-asked-questions/">FAQ</a> </li> <li class="general-help"> <a href="/general-help/">General Help</a> </li> <li class="reviewer-service"> <a href="https://zbmath.org/reviewer-service/" target="_self" >Reviewer Service</a> </li> <li> <a href="/tools-and-resources/">Tools & Resources</a> </li> <li class="contact"> <a href="/contact/">Contact</a> </li> </ul> <ul class="nav navbar-nav navbar-right prefs"> <li class="preferences dropdown"> <a data-toggle="dropdown" href="#">Preferences <i class="caret"></i></a> <ul class="dropdown-menu preferences"> <li> <form id="preferences" class="navbar-form" method="post" action="/preferences/" onsubmit="return confirm('This website uses cookies for the purposes of storing preference information on your device. Do you agree to this?\n\nPlease refer to our Privacy Policy to learn more about our use of cookies.')" > <input type="hidden" name="path" value="/1482.74083?"> <span class=""> <label class="title">Search Form</label> <div class="form-group"> <input id="search-multi-line" type="radio" name="search" value="multi-line" checked> <label for="search-multi-line" class="radio">Multi-Line Search (default)</label> </div> <div class="form-group"> <input id="search-one-line" type="radio" name="search" value="one-line"> <label for="search-one-line" class="radio">One-Line Search</label> </div> </span> <span class="count"> <label class="title">Hits per Page</label> <div class="form-group"> <input id="count-10" type="radio" name="count" value="10"> <label for="count-10" class="radio">10</label> </div> <div class="form-group"> <input id="count-20" type="radio" name="count" value="20"> <label for="count-20" class="radio">20</label> </div> <div class="form-group"> <input id="count-50" type="radio" name="count" value="50"> <label for="count-50" class="radio">50</label> </div> <div class="form-group"> <input id="count-100" type="radio" name="count" value="100" checked> <label for="count-100" class="radio">100 (default)</label> </div> <div class="form-group"> <input id="count-200" type="radio" name="count" value="200"> <label for="count-200" class="radio">200</label> </div> </span> <span class="format"> <label class="title">Display Format</label> <div class="form-group"> <input id="format-mathjax" type="radio" name="format" value="mathjax" checked> <label for="format-mathjax" class="radio">MathJax (default)</label> </div> <div class="form-group"> <input id="format-amstex" type="radio" name="format" value="latex"> <label for="format-amstex" class="radio">LaTeX</label> </div> </span> <span class="ranking"> <label class="title">Documents Sorting</label> <div class="form-group"> <input id="documents-ranking-default" type="radio" name="documents_ranking" value="date" checked> <label for="documents-ranking-default" class="radio">Newest first (default)</label> </div> <div class="form-group"> <input id="documents-ranking-references" type="radio" name="documents_ranking" value="references"> <label for="documents-ranking-references" class="radio">Citations</label> </div> <div class="form-group"> <input id="documents-ranking-relevance" type="radio" name="documents_ranking" value="relevance"> <label for="documents-ranking-relevance" class="radio">Relevance</label> </div> </span> <span class="ranking"> <label class="title">Authors Sorting</label> <div class="form-group"> <input id="authors-ranking-default" type="radio" name="authors_ranking" value="alpha" checked> <label for="authors-ranking-default" class="radio">Alphabetically (default)</label> </div> <div class="form-group"> <input id="authors-ranking-references" type="radio" name="authors_ranking" value="references"> <label for="authors-ranking-references" class="radio">Citations</label> </div> </span> <span class="ranking"> <label class="title">Serials Sorting</label> <div class="form-group"> <input id="serials-ranking-default" type="radio" name="serials_ranking" value="alpha" checked> <label for="serials-ranking-default" class="radio">Alphabetically (default)</label> </div> <div class="form-group"> <input id="serials-ranking-references" type="radio" name="serials_ranking" value="references"> <label for="serials-ranking-references" class="radio">Citations</label> </div> </span> <span class="ranking"> <label class="title">Software Sorting</label> <div class="form-group"> <input id="software-ranking-default" type="radio" name="software_ranking" value="references" checked> <label for="software-ranking-default" class="radio">Citations (default)</label> </div> <div class="form-group"> <input id="software-ranking-alpha" type="radio" name="software_ranking" value="alpha"> <label for="software-ranking-alpha" class="radio">Alphabetically</label> </div> </span> <button type="submit" class="btn btn-default">OK</button> <div class="clearfix"> </form> </li> </ul> </li> </ul> </div> </div> </nav> <div id="tabs"> <h1 class="logo"> <a class="logo" href="/"> <img class="logo" src="/static/zbmath.gif" alt="zbMATH Open — the first resource for mathematics" > </a> </h1> <nav> <ul class="nav nav-tabs"> <li class="tab-documents active"> <a href="/">Documents</a> </li> <li class="tab-authors"> <a href="/authors/">Authors</a> </li> <li class="tab-serials"> <a href="/serials/">Serials</a> </li> <li class="tab-software"> <a href="/software/">Software</a> </li> <li class="tab-classification"> <a href="/classification/">Classification</a> </li> <li class="tab-formulae"> <a href="/formulae/">Formulæ</a> </li> </ul> </nav> <div class="clearfix"></div> </div> <div class="content-fixed"> <div class="content-formular"> <div style="display: none;"> <div class="row ml-0"id="multi-line-new-line" style="display: none;"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-0-f" aria-label="field"> <option data-type="input" value="any" selected>Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-0-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input"> <span class="multi-line-value" id="multi-line-type-range"><span style="padding-left: 5px;">from</span> <input name="ml-0-v1" class="form-control multi-line-input" type="text" value="" aria-label="value"> until <input name="ml-0-v2" class="form-control multi-line-input" type="text" value="" aria-label="value"></span> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-la" placeholder="use name or ISO code"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-rv" placeholder="enter name or zbMATH reviewer number"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-an" placeholder="Zbl, JFM or ERAM number"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-en" placeholder="e.g. DOI, ISBN, arXiv ID"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-sw" placeholder="use * to find all documents using software"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-br" placeholder="find documents about the life or work of a person"> <span class="multi-line-value" id="multi-line-type-multiselect-db"> <select class="multi-line-selectpicker" data-width="100%" multiple> <option value="zbl">Zbl</option> <option value="arxiv">arXiv</option> <option value="jfm">JFM</option> <option value="eram">ERAM</option> </select> <input type="hidden" class="multi-line-input" name="ml-0-v" value=""> </span> </div> <form name="documents" method="GET" action="/" autocomplete="off"> <div class="documents multi-line" style="display: none;"> <div class="forms"> <ul class="nav forms"> <li class="one-line"> <span tabindex="0" class="glyphicon glyphicon-question-sign" title="One-Line Search allows for free logical combinations of search fields" aria-label="One-Line Search allows for free logical combinations of search fields" data-placement="bottom"></span> <a style="display: inline-block;" href="#">One-Line Search <span class="glyphicon glyphicon-search"></span></a> </li> </ul> </div> <div class="clearfix"></div> <div class="container-fluid"> <input type="hidden" id="multi-line-ml" name="ml" value="3"> <div id="multi-line-row-wrapper"> <div class="row ml-1"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-1-f" aria-label="field"> <option data-type="input" value="any" selected>Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-1-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-1-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <div class="row ml-2"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-2-f" aria-label="field"> <option data-type="input" value="any">Anywhere</option> <option data-type="input" value="au" selected>Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-2-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-2-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <div class="row ml-3"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-3-f" aria-label="field"> <option data-type="input" value="any">Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti" selected>Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-3-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><div id="multi-line-plus"> <a href="#"><span class="glyphicon glyphicon-plus" aria-hidden="true"></span> add line</a> </div></div> </div> </div> <div class="row"> <div class="col-xs-12 form-inline"> <div class="form-group field checkboxes-wrapper" id="checkboxes-wrapper-test" style="visibility: hidden; position: fixed;"> <label>Document Type:</label> <div class="checkboxes"> <div class="slider"> <label title="search for Articles in Journals"> <input type="checkbox" class="form-control" value="j" checked> <span tabindex="0"><small></small></span> Journal Articles </label> </div> <div class="slider"> <label title="search for Articles in Conference Proceedings and Collected Volumes"> <input type="checkbox" class="form-control" value="a" checked> <span tabindex="0"><small></small></span> Collection Articles </label> </div> <div class="slider"> <label title="search for Monographs, Proceedings, Dissertations etc."> <input type="checkbox" class="form-control" value="b" checked> <span tabindex="0"><small></small></span> Books </label> </div> <div class="slider"> <label title="search for arXiv Preprints"> <input type="checkbox" class="form-control" value="p" checked> <span tabindex="0"><small></small></span> arXiv Preprints </label> </div> </div> </div> <div class="form-group field checkboxes-wrapper" id="checkboxes-wrapper-real"> <label>Document Type:</label> <div class="checkboxes"> <div class="slider"> <label for="dt-j" title="search for Articles in Journals"> <input type="checkbox" id="dt-j" name="dt" class="form-control" value="j" checked> <span tabindex="0"><small></small></span> Journal Articles </label> </div> <div class="slider"> <label for="dt-a" title="search for Articles in Conference Proceedings and Collected Volumes"> <input type="checkbox" id="dt-a" name="dt" class="form-control" value="a" checked> <span tabindex="0"><small></small></span> Collection Articles </label> </div> <div class="slider"> <label for="dt-b" title="search for Monographs, Proceedings, Dissertations etc."> <input type="checkbox" id="dt-b" name="dt" class="form-control" value="b" checked> <span tabindex="0"><small></small></span> Books </label> </div> <div class="slider"> <label for="dt-p" title="search for arXiv Preprints"> <input type="checkbox" id="dt-p" name="dt" class="form-control" value="p" checked> <span tabindex="0"><small></small></span> arXiv Preprints </label> </div> </div> </div> </div> </div> <div class="row"> <div class="col-xs-12 buttons"> <a tabindex="0" class="btn btn-default clear-all">Reset all <span class="glyphicon glyphicon-remove"></span></a> <div class="submit"> <button class="btn btn-default search" type="submit">Search <span class="glyphicon glyphicon-search"></span></button> </div> </div> </div> </div> </div> </form> <form class="form-inline" name="documents" method="GET" action="/"> <div class="documents one-line" style="display: block;"> <div class="forms"> <ul class="nav forms"> <li class="multi-line"><a href="#">New Multi-Line Search <span class="glyphicon glyphicon-list"></span></a></li> </ul> </div> <div id="search-row" class="input-group box"> <span> <div id="search-field"> <input class="query form-control" type="text" name="q" value="an:1482.74083" aria-label="Search for documents" placeholder="Search for documents" autocomplete="off"> </div> <div class="search-buttons input-group-btn"> <div class="btn-group"> <button class="btn btn-default search" type="submit"><span class="virtual">Search</span> <span class="glyphicon glyphicon-search" style="top: 2px;"></span></button> </div> </div> </span> <span> <div class="search-buttons input-group-btn"> <div class="btn-group"> <div class="btn-group fields"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Fields <i class="caret"></i></button> <ul id="fields" class="dropdown-menu pull-right"> <li><a href="#"><span class="token item">any:</span><span> </span>anywhere (default)</a></li> <li><a href="#"><span class="token item">ab:</span><span>  </span>review text</a></li> <li><a href="#"><span class="token item">an:</span><span>  </span>zbmath id</a></li> <li><a href="#"><span class="token item">any:</span><span>  </span>anywhere</a></li> <li><a href="#"><span class="token item">au:</span><span>  </span>contributor name</a></li> <li><a href="#"><span class="token item">br:</span><span>  </span>biographic reference name</a></li> <li><a href="#"><span class="token item">cc:</span><span>  </span>msc title</a></li> <li><a href="#"><span class="token item">dt:</span><span>  </span>document type</a></li> <li><a href="#"><span class="token item">doi:</span><span>  </span>doi</a></li> <li><a href="#"><span class="token item">en:</span><span>  </span>external id</a></li> <li><a href="#"><span class="token item">la:</span><span>  </span>language</a></li> <li><a href="#"><span class="token item">pu:</span><span>  </span>publisher</a></li> <li><a href="#"><span class="token item">py:</span><span>  </span>year</a></li> <li><a href="#"><span class="token item">rv:</span><span>  </span>reviewer name</a></li> <li><a href="#"><span class="token item">so:</span><span>  </span>source</a></li> <li><a href="#"><span class="token item">sw:</span><span>  </span>software name</a></li> <li><a href="#"><span class="token item">ti:</span><span>  </span>title</a></li> <li><a href="#"><span class="token item">ut:</span><span>  </span>keyword</a></li> </ul> </div> <div class="btn-group operators"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Operators <i class="caret"></i></button> <ul id="operators" class="dropdown-menu pull-right"> <li><a href="#"><span class="token">a <span class="item">&</span> b </span><span> </span>logical and (default)</a></li> <li><a href="#"><span class="token">a <span class="item">|</span> b </span><span> </span>logical or</a></li> <li><a href="#"><span class="token"><span class="item">!</span>ab   </span><span> </span>logical not</a></li> <li><a href="#"><span class="token">abc<span class="item">*</span>  </span><span> </span>right wildcard</a></li> <li><a href="#"><span class="token"><span class="item">"</span>ab c<span class="item">"</span></span><span> </span>phrase</a></li> <li><a href="#"><span class="token"><span class="item">(</span>ab c<span class="item">)</span></span><span> </span>parentheses</a></li> </ul> </div> </div> </div> <div class="special"> <ul class="nav help-button"> <li class="dropdown pull-right"> <a href="#">Help <i class="caret"></i></a> </li> </ul> </div> </span> </div> <div class="help"><h2>Examples</h2> <div id="help-terms" role="table"> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Geometry">Geometry</a></span> <span class="search-explanation" role="cell" role="cell">Search for the term <em>Geometry</em> in <strong>any</strong> field. Queries are <strong>case-independent</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Funct%2A">Funct*</a></span> <span class="search-explanation" role="cell"><strong>Wildcard</strong> queries are specified by <strong><u>*</u></strong> (e.g. <em>functions</em>, <em>functorial</em>, etc.). Otherwise the search is <strong>exact</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Topological+group%22">"Topological group"</a></span> <span class="search-explanation" role="cell"><strong>Phrases</strong> (multi-words) should be set in <u>"</u>straight quotation marks<u>"</u>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=au%3A+Bourbaki+%26+ti%3A+Algebra">au: Bourbaki & ti: Algebra</a></span> <span class="search-explanation" role="cell">Search for <strong><u>au</u>thor</strong> and <strong><u>ti</u>tle</strong>. The <strong>and-operator &</strong> is default and can be omitted.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Chebyshev+%7C+Tschebyscheff">Chebyshev | Tschebyscheff</a></span> <span class="search-explanation" role="cell">The <strong>or-operator |</strong> allows to search for <em>Chebyshev</em> or <em>Tschebyscheff</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Quasi%2A+map%2A+py%3A+1989">Quasi* map* py: 1989</a></span> <span class="search-explanation" role="cell">The resulting documents have <strong><u>p</u>ublication <u>y</u>ear</strong> <em>1989</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=so%3A+Eur%2A+J%2A+Mat%2A+Soc%2A+cc%3A+14">so: Eur* J* Mat* Soc* cc: 14</a></span> <span class="search-explanation" role="cell">Search for publications in a particular <strong><u>so</u>urce</strong> with a <strong>Mathematics Subject <u>C</u>lassification <u>c</u>ode (<u>cc</u>)</strong> in <em>14</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Partial+diff%2A+eq%2A%22+%21+elliptic">"Partial diff* eq*" ! elliptic</a></span> <span class="search-explanation" role="cell">The <strong>not</strong>-operator <strong>!</strong> eliminates all results containing the word <em>elliptic</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=dt%3A+b+%26+au%3A+Hilbert">dt: b & au: Hilbert</a></span> <span class="search-explanation" role="cell">The <strong><u>d</u>ocument <u>t</u>ype</strong> is set to books; alternatively: <u>j</u> for <strong>journal articles</strong>, <u>a</u> for <strong>book articles</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=py%3A+2000-2015+cc%3A+%2894A+%7C+11T%29">py: 2000-2015 cc: (94A | 11T)</a></span> <span class="search-explanation" role="cell">Number <strong>ranges</strong> are accepted. Terms can be grouped within <strong><u>(</u>parentheses<u>)</u></strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=la%3A+chinese">la: chinese</a></span> <span class="search-explanation" role="cell">Find documents in a given <strong><u>la</u>nguage</strong>. <a href="http://en.wikipedia.org/wiki/ISO_639-1">ISO 639-1</a> language codes can also be used.</span> </div> </div> <div id="help-fields"> <h2>Fields</h2> <table> <tr> <td class="nowrap padding" role="rowheader"><strong>any</strong></td> <td class="padding">anywhere</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>an</strong></td> <td class="padding">internal document identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>au</strong></td> <td class="padding">author, editor</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ai</strong></td> <td class="padding">internal author identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ti</strong></td> <td class="padding">title</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>la</strong></td> <td class="padding">language</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>so</strong></td> <td class="padding">source</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ab</strong></td> <td class="padding">review, abstract</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>py</strong></td> <td class="padding">publication year</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>rv</strong></td> <td class="padding">reviewer</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>cc</strong></td> <td class="padding">MSC code</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ut</strong></td> <td class="padding">uncontrolled term</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>dt</strong></td> <td class="padding" colspan="4">document type (<strong>j</strong>: journal article; <strong>b</strong>: book; <strong>a</strong>: book article)</td> </tr> </table> </div> <div id="help-operators"> <h2>Operators</h2> <table> <tr> <td class="nowrap padding" role="rowheader">a <strong>&</strong> b</td> <td class="padding">logic and</td> </tr> <tr> <td class="nowrap padding" role="rowheader">a <strong>|</strong> b</td> <td class="padding">logic or</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>!</strong>ab</td> <td class="padding">logic not</td> </tr> <tr> <td class="nowrap padding" role="rowheader">abc<strong>*</strong></td> <td class="padding">right wildcard</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>"</strong>ab c<strong>"</strong></td> <td class="padding">phrase</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>(</strong>ab c<strong>)</strong></td> <td class="padding">parentheses</td> </tr> </table> </div> <p> See also our <a href="/general-help/">General Help</a>. </p></div> </div> </form> <div class="clearfix"></div> </div> <div class="content-shadow"></div> </div> </div> <div id="body"> <div id="main"> <div class="messages"> </div> <div id="documents"> <div class="content-main"> <div class="content-item"><div class="item"> <article> <div class="author"><a href="/authors/he.chun-hui" title="Author Profile">He, Chun-Hui</a>; <a href="/authors/liu.chao" title="Author Profile">Liu, Chao</a>; <a href="/authors/he.ji-huan" title="Author Profile">He, Ji-Huan</a>; <a href="/authors/gepreel.khaled-a" title="Author Profile">Gepreel, Khaled A.</a></div> <h2 class="title"> <strong>Low frequency property of a fractal vibration model for a concrete beam.</strong> <i>(English)</i> <a class="label nowrap" href="/1482.74083">Zbl 1482.74083</a> </h2> <div class="source"> <a href="/serials/2026" title="Journal Profile">Fractals</a> <a href="/?q=in%3A475628" title="Articles in this Issue">29, No. 5, Article ID 2150117, 7 p. (2021)</a>. </div> <div class="abstract">Summary: A concrete beam is a basic element for many applications in architectural engineering, and its vibration property plays an important role in safety and life-span. Previous vibration models were based on continuum beam theories, which could not take into account the porous property of the concrete beam. This paper adopts a two-scale fractal vibration model, and its low frequency property is revealed. This new finding can explain the vibration attenuation and vibration absorption of the porous concrete, and the present theory sheds a new light on the concrete design.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7465638">Cited in <strong>17</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A74H45" title="MSC2020">74H45</a> </td> <td class="space"> Vibrations in dynamical problems in solid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74K10" title="MSC2020">74K10</a> </td> <td class="space"> Rods (beams, columns, shafts, arches, rings, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74F10" title="MSC2020">74F10</a> </td> <td class="space"> Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74H10" title="MSC2020">74H10</a> </td> <td class="space"> Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A28A80" title="MSC2020">28A80</a> </td> <td class="space"> Fractals </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3ABernoulli-Euler+porous+beam+model">Bernoulli-Euler porous beam model</a>; <a href="/?q=ut%3Avibration+attenuation">vibration attenuation</a>; <a href="/?q=ut%3Atwo-scale+fractal+derivative">two-scale fractal derivative</a>; <a href="/?q=ut%3Afractal+oscillator">fractal oscillator</a>; <a href="/?q=ut%3Avariational+principle">variational principle</a>; <a href="/?q=ut%3Ahomotopy+perturbation+method">homotopy perturbation method</a>; <a href="/?q=ut%3Aperiodic+solution">periodic solution</a>; <a href="/?q=ut%3Aresonance">resonance</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1482.74083" data-ciurl="/ci/07465638" data-biburl="/bibtex/07465638.bib" data-amsurl="/amsrefs/07465638.bib" data-xmlurl="/xml/07465638.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07465638.pdf" title="Zbl 1482.74083 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1142/S0218348X21501176" aria-label="DOI for “Low frequency property of a fractal vibration model for a concrete beam”" title="10.1142/S0218348X21501176">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Kalfat, R., Al-Mahaidi, R. and Smith, S. T., Anchorage devices used to improve the performance of reinforced concrete beams retrofitted with FRP composites: State-of-the-art review, J. Compos. Constr.17(1) (2013) 14-33.</td> </tr><tr> <td>[2]</td> <td class="space">Sadek, F.et al., Testing and analysis of steel and concrete beam-column assemblies under a column removal scenario, J. Struct. Eng.-ASCE137(9) (2011) 881-892.</td> </tr><tr> <td>[3]</td> <td class="space">Yoo, D.-Y. and Yoon, Y.-S., Structural performance of ultra-high-performance concrete beams with different steel fibers, Eng. Struct.102 (2015) 409-423.</td> </tr><tr> <td>[4]</td> <td class="space">Ombres, L., Flexural analysis of reinforced concrete beams strengthened with a cement based high strength composite material, Compos. Struct.94(1) (2011) 143-155.</td> </tr><tr> <td>[5]</td> <td class="space">Attari, N., Amziane, S. and Chemrouk, M., Flexural strengthening of concrete beams using CFRP, GFRP and hybrid FRP sheets, Constr. Build. Mater.37 (2012) 746-757.</td> </tr><tr> <td>[6]</td> <td class="space">Yu, J. and Tan, K. H., Experimental and numerical investigation on progressive collapse resistance of reinforced concrete beam column sub-assemblages, Eng. Struct.55 (2013) 90-106.</td> </tr><tr> <td>[7]</td> <td class="space">Niesterowicz, B., Dunaj, P. and Berczynski, S., Timoshenko beam model for vibration analysis of composite steel-polymer concrete box beams, J. Theor. Appl. Mech.58(3) (2020) 799-810.</td> </tr><tr> <td>[8]</td> <td class="space">Wang, J., Ren, J. and Zhang, Y., Vibration analysis of carbon fiber-reinforced steel-concrete composite beams considering shear-slip effects, Int. J. Struct. Stabil. Dyn.19(7) (2019) 1950077.</td> </tr><tr> <td>[9]</td> <td class="space">Karnovsky, I. A. and Lebed, O. I., Non-Classical Vibrations of Arches and Beams: Eigenvalues and Eigenfunctions (McGraw-Hill, New York, 2004).</td> </tr><tr> <td>[10]</td> <td class="space">He, J. H., Generalized variational principles for buckling analysis of circular cylinders, Acta Mech.231(5) (2020) 899-906. · <a href="/1434.74058" class="nowrap">Zbl 1434.74058</a></td> </tr><tr> <td>[11]</td> <td class="space">Tian, D.et al., Fractal N/MEMS: From pull-in instability to pull-in stability, Fractals29(2) (2020) 2150030, https://doi.org/10.1142/S0218348X21500304. · <a href="/1481.78002" class="nowrap">Zbl 1481.78002</a></td> </tr><tr> <td>[12]</td> <td class="space">Ji, F. Y.et al., A fractal Boussinesq equation for nonlinear transverse vibration of a nanofiber-reinforced concrete pillar, Appl. Math. Model.82 (2020) 437-448. · <a href="/1481.74266" class="nowrap">Zbl 1481.74266</a></td> </tr><tr> <td>[13]</td> <td class="space">Jin, X., Liu, M., Pan, F., Li, Y. and Fan, J., Low frequency of a deforming capillary vibration, part 1: Mathematical model, J. Low Freq. Noise Vib. Act. Control38(3-4) (2019) 1676-1680.</td> </tr><tr> <td>[14]</td> <td class="space">He, J. and Jin, X., A short review on analytical methods for the capillary oscillator in a nanoscale deformable tube, Math. Methods Appl. Sci.30(11) (2020) 4933-4943, https://doi.org/10.1002/mma.6321.</td> </tr><tr> <td>[15]</td> <td class="space">He, C.-H., He, J.-H. and Sedighi, H. M., Fangzhu : An ancient Chinese nanotechnology for water collection from air: History, mathematical insight, promises, and challenges, Math. Methods Appl. Sci. (2020), https://doi.org/10.1002/mma.6384.</td> </tr><tr> <td>[16]</td> <td class="space">Wang, K. L., Effect of Fangzhu’s nano-scale surface morphology on water collection, Math. Methods Appl. Sci. (2020), https://doi.org/10.1002/mma.6569.</td> </tr><tr> <td>[17]</td> <td class="space">He, J.-H. and El-Dib, Y. O., Homotopy perturbation method for Fangzhu oscillator, J. Math. Chem.58(10) (2020) 2245-2253. · <a href="/1470.34050" class="nowrap">Zbl 1470.34050</a></td> </tr><tr> <td>[18]</td> <td class="space">He, C. H., Liu, C., He, J. H., Shirazi, A. H. and Mohammad-Sedighi, H., Passive Atmospheric water harvesting utilizing an ancient Chinese ink slab and its possible applications in modern architecture, FU Mech. Eng. (2021), https://doi.org/10.22190/FUME201203001H.</td> </tr><tr> <td>[19]</td> <td class="space">He, J. H. and Ain, Q. T., New promises and future challenges of fractal calculus: From two-scale thermodynamics to fractal variational principle, Therm. Sci.24(2A) (2020) 659-681.</td> </tr><tr> <td>[20]</td> <td class="space">Ain, Q. T. and He, J. H., On two-scale dimension and its applications, Therm. Sci.23(3) (2019) 1217-1219, https://doi.org/10.2298/TSCI2102217H.</td> </tr><tr> <td>[21]</td> <td class="space">He, J. H., Fractal calculus and its geometrical explanation, Results Phys.10 (2018) 272-276.</td> </tr><tr> <td>[22]</td> <td class="space">He, J.-H., Seeing with a single scale is always unbelieving: From magic to two-scale fractal, Therm. Sci.25(2B) (2021) 1217-1219, https://doi.org/10.2298/TSCI2102217H.</td> </tr><tr> <td>[23]</td> <td class="space">Zuo, Y. T. and Liu, H. J., A fractal rheological model for SiC paste using a fractal derivative, J. Appl. Comput. Mech.7 (2021) 13-18.</td> </tr><tr> <td>[24]</td> <td class="space">Zuo, Y. T., Effect of SiC particles on viscosity of 3D print paste: A fractal rheological model and experimental verification, Therm. Sci.25(3B) (2021) 2405-2409, https://doi.org/10.2298/TSCI200710131Z.</td> </tr><tr> <td>[25]</td> <td class="space">Zuo, Y. T. and Liu, H. J., Fractal approach to the mechanical and electronical properties of SiC/graphene composites, FU Mech. Eng. (2021), https://doi.org/10.22190/FUME123456001A.</td> </tr><tr> <td>[26]</td> <td class="space">Xu, L. Y., Li, Y., Li, X. X. and He, J. H., Detection of cigarette smoke using a fiber membrane filmed with carbon nanoparticles and a fractal current law, Therm. Sci.24(4) (2020) 2469-2474.</td> </tr><tr> <td>[27]</td> <td class="space">Liu, F. J., Zhang, X. J. and Li, X., Silkworm (Bombyx mori) cocoon vs. wild cocoon multi-layer structure and performance characterization, Therm. Sci.23(4) (2019) 2135-2142.</td> </tr><tr> <td>[28]</td> <td class="space">Wang, Y., Yao, S. W. and Yang, H. W., A fractal derivative model for snow’s thermal insulation property, Therm. Sci.23(4) (2019) 2351-2354.</td> </tr><tr> <td>[29]</td> <td class="space">Fan, J., Yang, X. and Liu, Y., Fractal calculus for analysis of wool fiber: Mathematical insight of its biomechanism, J. Eng. Fibers Fabr.14 (2019), https://doi.org/10.1177/1558925019872200.</td> </tr><tr> <td>[30]</td> <td class="space">Wang, Q. L.et al., Fractal calculus and its application to explanation of biomechanism of polar bear hairs, Fractals27(5) (2019) 1992001.</td> </tr><tr> <td>[31]</td> <td class="space">Wang, Q. L.et al., Fractal calculus and its application to explanation of biomechanism of polar bear hairs, Fractals26(6) (2018) 1850086.</td> </tr><tr> <td>[32]</td> <td class="space">He, C. H.et al., Taylor series solution for fractal Bratu-type equation arising in electrospinning process, Fractals28(1) (2020) 2050011.</td> </tr><tr> <td>[33]</td> <td class="space">Lin, L. and Yao, S. W., Fractal diffusion of silver ions in hollow cylinders with unsmooth inner surface, J. Eng. Fibers Fabr.14 (2019), https://doi.org/1558925019895643.</td> </tr><tr> <td>[34]</td> <td class="space">Li, X. J., Liu, Z. and He, J. H., A fractal two-phase flow model for the fiber motion in a polymer filling process, Fractals (2020), https://doi.org/10.1142/S0218348X20500930.</td> </tr><tr> <td>[35]</td> <td class="space">He, J. H., A simple approach to one-dimensional convection-diffusion equation and its fractional modification for E reaction arising in rotating disk electrodes, J. Electroanal. Chem.854 (2019) 113565.</td> </tr><tr> <td>[36]</td> <td class="space">Anjum, N. and Ain, Q. T., Application of he’s fractional derivative and fractional complex transform for time fractional Camassa-Holm equation, Therm. Sci.24(5A) (2020) 3023-3030.</td> </tr><tr> <td>[37]</td> <td class="space">Wang, K. L., A new fractal model for the soliton motion in a microgravity space. Int. J. Numer. Methods Heat Fluid Flow (2020), https://doi.org/10.1108/HFF-05-2020-0247.</td> </tr><tr> <td>[38]</td> <td class="space">Wang, K. L. and Wei, C. F., A powerful and simple frequency formula to nonlinear fractal oscillators, J. Low Freq. Noise Vib. Act. Control (2020), https://doi.org/10.1177/1461348420947832.</td> </tr><tr> <td>[39]</td> <td class="space">Alex, E. Z.et al., Equivalent power-form representation of the fractal Toda oscillator, Fractals (2020), https://doi.org/10.1142/S0218348X21500341. · <a href="/1481.78022" class="nowrap">Zbl 1481.78022</a></td> </tr><tr> <td>[40]</td> <td class="space">Alex, E. Z., Lius, M. P. P., Isaac, H. J. C., Oscar, M. R. and Daniel, O. T., He’s frequency-amplitude formulation for nonlinear oscillators using Jacobi elliptic functions, J. Low Freq. Noise Vib. Act. Control (2020), https://doi.org/10.1177/1461348420972820.</td> </tr><tr> <td>[41]</td> <td class="space">Elias-Zuniga, A., Palacios-Pineda, L.M., Jiménez-Cedeño, I.H., Martínez-Romero, O. and Olvera-Trejo, D., A fractal model for current generation in porous electrodes, J. Electroanal. Chem. (2021) 880, https://doi.org/1016/2020.114883.</td> </tr><tr> <td>[42]</td> <td class="space">He, J. H., Qie, N., He, C. H. and Saeed, T., On a strong minimum condition of a fractal variational principle, Appl. Math. Lett.119 (2021) 107199. · <a href="/1538.49025" class="nowrap">Zbl 1538.49025</a></td> </tr><tr> <td>[43]</td> <td class="space">He, J. H., A fractal variational theory for one-dimensional compressible flow in a microgravity space, Fractals28(2) (2020) 20500243.</td> </tr><tr> <td>[44]</td> <td class="space">Wang, K. L. and Yao, S. W., Fractal variational theory for Chaplygin-He Gas in a microgravity condition, Comput. Methods Appl. Mech. Eng.6(SI) (2020) 1606-1612.</td> </tr><tr> <td>[45]</td> <td class="space">J. H. He, On the fractal variational principle for the Telegraph equation, Fractals, doi:10.1142/S0218348X21500225. · <a href="/1482.35005" class="nowrap">Zbl 1482.35005</a></td> </tr><tr> <td>[46]</td> <td class="space">Qie, N., Hou, W.-F. and He, J.-H., The fastest insight into the large amplitude vibration of a string, Rep. Mech. Eng.2(1) (2020) 1-5, https://doi.org/10.31181/rme200102001q.</td> </tr><tr> <td>[47]</td> <td class="space">He, J.-H., Hou, W.-F., Qie, N., Gepreel, K. A., Shirazi, A. H. and Sedighi, H. M., Hamiltonian-based frequency-amplitude formulation for nonlinear oscillators, FU Mech. Eng. (2021), https://doi.org/10.22190/FUME 201205002H.</td> </tr><tr> <td>[48]</td> <td class="space">He, J. H., Some asymptotic methods for strongly nonlinear equations, Int. J. Mod. Phys. B20(10) (2006) 1141-1199. · <a href="/1102.34039" class="nowrap">Zbl 1102.34039</a></td> </tr><tr> <td>[49]</td> <td class="space">A. Elias-Zuniga, L. M. Palacios-Pineda, I. H. Jimenez-Cedeno, O. Martinez-Romero and D. O. Trejo, Analytical solution of the fractal cubic-quintic duffing equation, Fractals, https://doi.org/10.1142/S0218348X21500808. · <a href="/1489.34002" class="nowrap">Zbl 1489.34002</a></td> </tr><tr> <td>[50]</td> <td class="space">Zuo, Y.-T., A gecko-like fractal receptor of a three-dimensional printing technology: A fractal oscillator, J. Math. Chem. (2021), https://doi.org/10.1007/s10910-021-01212-y. · <a href="/1466.92309" class="nowrap">Zbl 1466.92309</a></td> </tr><tr> <td>[51]</td> <td class="space">He, J.-H., Kou, S.-J., He, C.-H., Zhang, Z.-W. and Gepreel, K. A., Fractal oscillation and its frequency-amplitude property, Fractals (2020), https://doi.org/10.1142/S0218348X2150105X. · <a href="/1489.34014" class="nowrap">Zbl 1489.34014</a></td> </tr><tr> <td>[52]</td> <td class="space">He, J.-H., Moatimid, G. M. and Mostapha, D. R., Nonlinear instability of two streaming-superposed magnetic Reiner-Rivlin fluids by He-Laplace method, J. Electroanal. Chem.895 (2021) 115388, https://doi.org/10.1016/j.jelechem.2021.115388.</td> </tr><tr> <td>[53]</td> <td class="space">He, C. H., Tian, D., Moatimid, G. M., Salman, H. F. and Zekry, M. H., Hybrid Rayleigh-Van der Pol-Duffing oscillator (HRVD): Stability analysis and controller, J. Low Freq. Noise Vib. Active Control (2021), https://doi.org/10.1177/14613484211026407.</td> </tr><tr> <td>[54]</td> <td class="space">He, J.-H. and El-Dib, Y. O., The reducing rank method to solve third-order Duffing equation with the homotopy perturbation, Numer. Methods Partial Differ. Equ.37(2) (2021) 1800-1808, https://doi.org/10.1002/num.22609. · <a href="/07776044" class="nowrap">Zbl 07776044</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

CINXE.COM

Document Zbl 1482.74083 - zbMATH Open